Resilient bus services design in a multimodal network with uncertain metro system disruption

Disruptions in the metro system often lead to chaos in the public transportation system due to their significant mode share. To mitigate such impacts, this study designs a multimodal public transportation network integrating metro and bus, subject to stochastic metro disruptions. With a given metro system, a two-stage stochastic programming model is formulated to design complementary bus services, catering to stochastically degradable metro capacity. Under normal metro operations, the bus services complement the metro services, but with built-in resiliency to handle potential disruptions. In the event of metro disruptions, they function as substitutes to mitigate the disruptive impact on passengers, thereby maintaining system reliability. The bus routings and service frequencies are designed to achieve social optimal by minimizing the combined costs of bus construction, operating expenses, expected total passenger costs, and unmet demand costs arising from metro disruptions. A service reliability-based solution method is adopted to solve the problem by decomposing the problem into two phases. In phase 1, given a service reliability measure, the model determines the bus routing and frequencies. Then, in phase 2, given the bus routes and frequencies, it minimizes the costs of lost demand and passenger inconvenience. A service overlapping penalty is considered to prevent substantial duplication between metro and bus services. The effectiveness of the proposed model is validated in a case study, demonstrating the advantages of considering stochastic degradable capacity and designing complementary bus services in an integrated multimodal public transportation system. Under various disruption conditions, the demand loss is reduced by over 95% compared tobenchmark cases.